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Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or…

Graph Neural Networks (GNNs) have emerged as powerful tools for learning representations of graph-structured data, demonstrating remarkable performance across various tasks. Recognising their importance, there has been extensive research…

Community detection in hypergraphs is both instrumental for functional module identification and intricate due to higher-order interactions among nodes. We define a hypergraph Ricci flow that directly operates on higher-order interactions…

We present the application of topological data analysis (TDA) to study unweighted complex networks via their persistent homology. By endowing appropriate weights that capture the inherent topological characteristics of such a network, we…

In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility…

Federated clustering addresses the critical challenge of extracting patterns from decentralized, unlabeled data. However, it is hampered by the flaw that current approaches are forced to accept a compromise between performance and privacy:…

Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…

Core-periphery structure is a common property of complex networks, which is a composition of tightly connected groups of core vertices and sparsely connected periphery vertices. This structure frequently emerges in traffic systems, biology,…

Identifying cliques in dense networks remains a formidable challenge, even with significant advances in computational power and methodologies. To tackle this, numerous algorithms have been developed to optimize time and memory usage,…

Randomly Wired Neural Networks (RWNNs) serve as a valuable testbed for investigating the impact of network topology in deep learning by capturing how different connectivity patterns impact both learning efficiency and model performance. At…

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It…

Graphs are ubiquitous to model the irregular (non-Euclidean) structure of complex data, but they are limited to pairwise relationships and fail to model the complexities of the datasets exhibiting higher-order interactions. In that context,…

We provide an overview of Forman-Ricci curvature and persistent homology, and how their combination can be applied to the study of networks. We discuss how the usually employed augmented Forman-Ricci curvature formula, only valid for…

Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named…

The block diagonal structure of an affinity matrix is a commonly desired property in cluster analysis because it represents clusters of feature vectors by non-zero coefficients that are concentrated in blocks. However, recovering a block…

We consider the problem of learning causal structures in sparse high-dimensional settings that may be subject to the presence of (potentially many) unmeasured confounders, as well as selection bias. Based on the structure found in common…

Despite the recent successes of vanilla Graph Neural Networks (GNNs) on various tasks, their foundation on pairwise networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this…

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

Clustering is an important data mining technique that groups similar data records, recently categorical transaction clustering is received more attention. In this research, we study the problem of categorical data clustering for…

The so called \v{C}ech and Vietoris-Rips simplicial filtrations are designed to capture information about the topological structure of metric datasets. These filtrations are two of the workhorses in the field of topological data analysis.…